Problem: Igor the analyst has adopted n little bunnies. As we all know, bunnies love carrots. Thus, Igor has bought a carrot to be shared between his bunnies. Igor wants to treat all the bunnies equally, and thus he wants to cut the carrot into n pieces of equal area. 

Formally, the carrot can be viewed as an isosceles triangle with base length equal to 1 and height equal to h. Igor wants to make n - 1 cuts parallel to the base to cut the carrot into n pieces. He wants to make sure that all n pieces have the same area. Can you help Igor determine where to cut the carrot so that each piece have equal area?

<image> Illustration to the first example.

Input

The first and only line of input contains two space-separated integers, n and h (2 ≤ n ≤ 1000, 1 ≤ h ≤ 105).

Output

The output should contain n - 1 real numbers x1, x2, ..., xn - 1. The number xi denotes that the i-th cut must be made xi units away from the apex of the carrot. In addition, 0 < x1 < x2 < ... < xn - 1 < h must hold. 

Your output will be considered correct if absolute or relative error of every number in your output doesn't exceed 10 - 6.

Formally, let your answer be a, and the jury's answer be b. Your answer is considered correct if <image>.

Examples

Input

3 2


Output

1.154700538379 1.632993161855


Input

2 100000


Output

70710.678118654752

Note

Definition of isosceles triangle: <https://en.wikipedia.org/wiki/Isosceles_triangle>.

Solution (in PYTHON3):

Solution:
import math
import sys


def trapezoid(top_angle, area, a):
    bot_angle = (math.pi - top_angle) / 2
    bot_side = (-a * math.sin(bot_angle) + math.sqrt(
        ((a * math.sin(bot_angle)) ** 2) + 4 * math.cos(bot_angle) * math.sin(bot_angle) * area)) / (
               2 * math.cos(bot_angle) * math.sin(bot_angle))
    return bot_side * math.sin(bot_angle)


if __name__ == '__main__':
    n, h = [int(num) for num in input().split()]
    triangle_area = 0.5 * h * 1
    part_area = triangle_area / n
    top_angle = 2 * math.atan(0.5 / h)
    top_side = math.sqrt(2 * part_area / math.sin(top_angle))
    top_height = top_side * math.cos(top_angle / 2)
    top_low_side = 2 * math.sqrt(top_side ** 2 - top_height ** 2)
    parts = []
    parts.append(top_height)
    h = top_height
    # bot = top_low_side
    s = ""
    for i in range(0, n - 2):
        # h_trap = trapezoid(top_angle, part_area, bot)
        h_trap = top_height * math.sqrt(i + 2)
        parts.append(h_trap)
        h = h_trap
        # bot = bot + h_trap * 2 / math.tan(math.pi - top_angle)
    for i in range(0, len(parts)):
        print(parts[i])